Finite Group Databasebeta

← C3×#10589794 #13153154

Subgroups — C3×#10589794 #13153154

Order 1728.

710 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C9×#125C211yesmaximal, characteristic, complemented
2C3×#63460C211yesmaximal, characteristic, complemented
3C3×#63459C211yesmaximal, characteristic, complemented
4C3×#63458C211yesmaximal, characteristic, complemented
5C3×#63458C211yesmaximal, characteristic, complemented
6C3×#63457C211yesmaximal, characteristic
7C3×#63456C211yesmaximal, characteristic, complemented
8C3×#63456C211yesmaximal, characteristic, complemented
9C3×#63456C211yesmaximal, characteristic, complemented
10C3×#63456C211yesmaximal, characteristic, complemented
11C3×#63455C211yesmaximal, characteristic, complemented
12C3×C4⋊C4×D9C211yesmaximal, characteristic, complemented
13C3×#63451C211yesmaximal, characteristic, complemented
14C3×#63438C211yesmaximal, characteristic, complemented
15C3×C4×D36C211yesmaximal, characteristic, complemented
16C3×#5692—31nomaximal
17#10589794C311yesmaximal, characteristic, direct product factor
18C2×C3×D36C2211yescharacteristic
19C2×C3×D36C2211yescharacteristic
20C2×C3×D36C2211yescharacteristic
21C2×C3×C4×D9C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic
26C2×C3×Dic18C2211yescharacteristic
27C3×C9×C4⋊C4C2211yescharacteristic
28C3×C9×C4⋊C4C2211yescharacteristic
29C3×C9×C4⋊C4C2211yescharacteristic
30C3×C9×C4⋊C4C2211yescharacteristic
31C3×C9×C4⋊C4C2211yescharacteristic
32C3×C9×C4⋊C4C2211yescharacteristic
33C3×C42×C9C2211yescharacteristic
34C3×(C2×D9)⋊C4C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×C4⋊Dic9C2211yescharacteristic
45C3×C4⋊Dic9C2211yescharacteristic
46C3×Dic9⋊C4C2211yescharacteristic
47C3×Dic9⋊C4C2211yescharacteristic
48C3×Dic9⋊C4C2211yescharacteristic
49C3×Dic9⋊C4C2211yescharacteristic
50C3×Dic9⋊C4C2211yescharacteristic
51C3×Dic9⋊C4C2211yescharacteristic
52C3×C4×Dic9C2211yescharacteristic
53C32×#125D311yescharacteristic
54C3×#898—31no—
55C3×#897—31no—
56C3×#896—31no—
57C3×#896—31no—
58C3×#895—31no—
59C3×#894—31no—
60C3×#894—31no—
61C3×#894—31no—
62C3×#894—31no—
63C3×#893—31no—
64C3×D3×C4⋊C4—31no—
65C3×#889—31no—
66C3×#876—31no—
67C3×C4×D12—31no—
68C9×#125—21no—
69C9×#125C2×C311yescharacteristic, complemented
70#63460C2×C311yescharacteristic, complemented
71#63459C2×C311yescharacteristic, complemented
72#63458C2×C311yescharacteristic, complemented
73#63458C2×C311yescharacteristic, complemented
74#63457C2×C311yescharacteristic
75#63456C2×C311yescharacteristic, complemented
76#63456C2×C311yescharacteristic, complemented
77#63456C2×C311yescharacteristic, complemented
78#63456C2×C311yescharacteristic, complemented
79#63455C2×C311yescharacteristic, complemented
80C4⋊C4×D9C2×C311yescharacteristic, complemented
81#63451C2×C311yescharacteristic, complemented
82#63438C2×C311yescharacteristic, complemented
83C4×D36C2×C311yescharacteristic, complemented
84C22×C3×D9C2311yescharacteristic
85C22×C3×D9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C2×C3×C4×C9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×Dic9C2311yescharacteristic
95C2×C3×Dic9C2311yescharacteristic
96C2×C3×Dic9C2311yescharacteristic
97C2×C3×Dic9C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C3×D36—22no—
100C3×D36—22no—
101C3×D36—41no—
102C3×C4×D9—22no—
103C3×C4×D9—41no—
104C3×C4×D9—41no—
105C3×C4×D9—41no—
106C3×C4×D9—41no—
107C3×Dic18—41no—
108C3×#539—91no—
109#5692—31no—
110C2×C3×D12—31no—
111C2×C3×D12—31no—
112C2×C3×D12—31no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—31no—
118C2×C3×Dic6—31no—
119C32×C4⋊C4C2×D311yescharacteristic
120C32×C4⋊C4C2×D311yescharacteristic
121C32×C4⋊C4C2×D311yescharacteristic
122C32×C4⋊C4C2×D311yescharacteristic
123C32×C4⋊C4C2×D311yescharacteristic
124C32×C4⋊C4C2×D311yescharacteristic
125C32×C42C2×D311yescharacteristic
126C3×(C2×D3)⋊C4—31no—
127C3×(C2×D3)⋊C4—31no—
128C3×(C2×D3)⋊C4—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4—31no—
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×C4⋊Dic3—31no—
137C3×C4⋊Dic3—31no—
138C3×Dic3⋊C4—31no—
139C3×Dic3⋊C4—31no—
140C3×Dic3⋊C4—31no—
141C3×Dic3⋊C4—31no—
142C3×Dic3⋊C4—31no—
143C3×Dic3⋊C4—31no—
144C3×C4×Dic3—31no—
145C2×D36C22×C311yescharacteristic
146C2×D36C22×C311yescharacteristic
147C2×D36C22×C311yescharacteristic
148C2×C4×D9C22×C311yescharacteristic
149C2×C4×D9C22×C311yescharacteristic
150C2×C4×D9C22×C311yescharacteristic
151C2×C4×D9C22×C311yescharacteristic
152C2×C4×D9C22×C311yescharacteristic
153C2×Dic18C22×C311yescharacteristic
154C9×C4⋊C4—21no—
155C9×C4⋊C4—21no—
156C9×C4⋊C4—21no—
157C9×C4⋊C4—21no—
158C9×C4⋊C4—21no—
159C9×C4⋊C4—21no—
160C9×C4⋊C4C22×C311yescharacteristic
161C9×C4⋊C4C22×C311yescharacteristic
162C9×C4⋊C4C22×C311yescharacteristic
163C9×C4⋊C4C22×C311yescharacteristic
164C9×C4⋊C4C22×C311yescharacteristic
165C9×C4⋊C4C22×C311yescharacteristic
166C42×C9—21no—
167C42×C9C22×C311yescharacteristic
168(C2×D9)⋊C4C22×C311yescharacteristic
169(C2×D9)⋊C4C22×C311yescharacteristic
170(C2×D9)⋊C4C22×C311yescharacteristic
171(C2×D9)⋊C4C22×C311yescharacteristic
172(C2×D9)⋊C4C22×C311yescharacteristic
173(C2×D9)⋊C4C22×C311yescharacteristic
174(C2×D9)⋊C4C22×C311yescharacteristic
175(C2×D9)⋊C4C22×C311yescharacteristic
176(C2×D9)⋊C4C22×C311yescharacteristic
177(C2×D9)⋊C4C22×C311yescharacteristic
178C4⋊Dic9C22×C311yescharacteristic
179C4⋊Dic9C22×C311yescharacteristic
180Dic9⋊C4C22×C311yescharacteristic
181Dic9⋊C4C22×C311yescharacteristic
182Dic9⋊C4C22×C311yescharacteristic
183Dic9⋊C4C22×C311yescharacteristic
184Dic9⋊C4C22×C311yescharacteristic
185Dic9⋊C4C22×C311yescharacteristic
186C4×Dic9C22×C311yescharacteristic
187C22×C3×C9C2411yescharacteristic
188C2×C3×D9—21no—
189C2×C3×D9—21no—
190C2×C3×D9—21no—
191C2×C3×D9—21no—
192C2×C3×D9—21no—
193C2×C3×D9—21no—
194C2×C3×D9—21no—
195C2×C3×D9—21no—
196C2×C3×D9#4112yes—
197C3×C4×C9—21no—
198C3×C4×C9—21no—
199C3×C4×C9—21no—
200C3×C4×C9—21no—
201C3×C4×C9—21no—
202C3×C4×C9—21no—
203C3×C4×C9—21no—
204C3×Dic9—21no—
205C3×Dic9—21no—
206C3×Dic9—21no—
207C3×Dic9—21no—
208C3×Dic9—21no—
209C3×#126—91no—
210C3×#126—91no—
211C3×#125—21no—
212C3×#125—91no—
213C3×#125D911yescharacteristic, complemented
214C3×#125C3×D311yescharacteristic
215C3×#123—91no—
216C3×#123—91no—
217C3×#123—91no—
218C3×#123—91no—
219C3×C22⋊Q8—91no—
220C3×C22⋊Q8—91no—
221C3×C22⋊Q8—91no—
222C3×#121—91no—
223C3×C4×D4—91no—
224C3×C4×D4—91no—
225C2×C3×C4⋊C4—91no—
226#898—31no—
227#897—31no—
228#896—31no—
229#896—31no—
230#895—31no—
231#894—31no—
232#894—31no—
233#894—31no—
234#894—31no—
235#893—31no—
236D3×C4⋊C4—31no—
237#889—31no—
238#876—31no—
239C4×D12—31no—
240C22×C3×D3—31no—
241C22×C3×D3—31no—
242C22×C3×D3—31no—
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245C2×C32×C4C22×D311yescharacteristic
246C2×C32×C4C22×D311yescharacteristic
247C2×C32×C4C22×D311yescharacteristic
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C3×Dic3—31no—
251C2×C3×Dic3—31no—
252C2×C3×Dic3—31no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—31no—
255C3×D12—62no—
256C3×D12—62no—
257C3×D12—121no—
258C3×C4×D3—62no—
259C3×C4×D3—121no—
260C3×C4×D3—121no—
261C3×C4×D3—121no—
262C3×C4×D3—121no—
263C3×Dic6—121no—
264C22×D9C23×C311yescharacteristic
265C22×D9C23×C311yescharacteristic
266C22×D9C23×C311yescharacteristic
267C2×C4×C9—21no—
268C2×C4×C9—21no—
269C2×C4×C9—21no—
270C2×C4×C9—21no—
271C2×C4×C9—21no—
272C2×C4×C9—21no—
273C2×C4×C9—21no—
274C2×C4×C9C23×C311yescharacteristic
275C2×C4×C9C23×C311yescharacteristic
276C2×C4×C9C23×C311yescharacteristic
277C2×C4×C9C23×C311yescharacteristic
278C2×C4×C9C23×C311yescharacteristic
279C2×C4×C9C23×C311yescharacteristic
280C2×C4×C9C23×C311yescharacteristic
281C2×Dic9C23×C311yescharacteristic
282C2×Dic9C23×C311yescharacteristic
283C2×Dic9C23×C311yescharacteristic
284C2×Dic9C23×C311yescharacteristic
285C2×Dic9C23×C311yescharacteristic
286D36—22no—
287D36—22no—
288D36—41no—
289C4×D9—22no—
290C4×D9—41no—
291C4×D9—41no—
292C4×D9—41no—
293C4×D9—41no—
294Dic18—41no—
295#539—91noSylow
296C2×C3×C9C2×#4111yescharacteristic
297C2×C3×C9H(5,𝔽2)11yescharacteristic
298C2×C3×C92−1+411yescharacteristic
299C3×D9—22no—
300C3×D9—41no—
301C3×D9—41no—
302C2×C3×Q8—91no—
303C2×C3×D4—91no—
304C2×C3×D4—91no—
305C2×C3×D4—91no—
306C22×C3×C4—91no—
307C22×C3×C4—91no—
308C22×C3×C4—91no—
309C22×C3×C4—91no—
310C22×C3×C4—91no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×Dic6—31no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—91no—
328C3×C4⋊C4—91no—
329C3×C4⋊C4—91no—
330C3×C4⋊C4—91no—
331C3×C4⋊C4—91no—
332C3×C4⋊C4—91no—
333C3×C4⋊C4—91no—
334C3×C4⋊C4C2×D911yescharacteristic
335C3×C4⋊C4C2×D911yescharacteristic
336C3×C4⋊C4C2×D911yescharacteristic
337C3×C4⋊C4C2×D911yescharacteristic
338C3×C4⋊C4C2×D911yescharacteristic
339C3×C4⋊C4C2×D911yescharacteristic
340C3×C4⋊C4C2×C3×D311yescharacteristic
341C3×C4⋊C4C2×C3×D311yescharacteristic
342C3×C4⋊C4C2×C3×D311yescharacteristic
343C3×C4⋊C4C2×C3×D311yescharacteristic
344C3×C4⋊C4C2×C3×D311yescharacteristic
345C3×C4⋊C4C2×C3×D311yescharacteristic
346C3×C22⋊C4—91no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349C3×C22⋊C4—91no—
350C3×C22⋊C4—91no—
351C3×C22⋊C4—91no—
352C3×C22⋊C4—91no—
353C3×C22⋊C4—91no—
354C3×C22⋊C4—91no—
355C3×C22⋊C4—91no—
356C3×C42—21no—
357C3×C42—91no—
358C3×C42C2×D911yescharacteristic
359C3×C42C2×C3×D311yescharacteristic
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372Dic3⋊C4—31no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—31no—
376Dic3⋊C4—31no—
377Dic3⋊C4—31no—
378C4×Dic3—31no—
379C22×C32C23×D311yescharacteristic
380C2×C3×D3—32no—
381C2×C3×D3—61no—
382C2×C3×D3—61no—
383C2×C3×D3—61no—
384C2×C3×D3—61no—
385C2×C3×D3—61no—
386C2×C3×D3—61no—
387C2×C3×D3—61no—
388C2×C3×D3—61no—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—21no—
396C3×Dic3—61no—
397C3×Dic3—61no—
398C3×Dic3—61no—
399C3×Dic3—61no—
400C3×Dic3—61no—
401C22×C9—21no—
402C22×C9C24×C311yescharacteristic
403C2×D9—21no—
404C2×D9—21no—
405C2×D9—21no—
406C2×D9—21no—
407C2×D9—21no—
408C2×D9—21no—
409C2×D9—21no—
410C2×D9—21no—
411C2×D9C3×#4112yes—
412C4×C9—22no—
413C4×C9—21no—
414C4×C9—21no—
415C4×C9—21no—
416C4×C9—21no—
417C4×C9—21no—
418C4×C9—21no—
419C4×C9—21no—
420C4×C9—41no—
421C4×C9—41no—
422C4×C9—41no—
423C4×C9—41no—
424C4×C9—41no—
425C4×C9—41no—
426Dic9—21no—
427Dic9—21no—
428Dic9—21no—
429Dic9—21no—
430Dic9—21no—
431#126—91no—
432#126—91no—
433#125—91no—
434#125C3×D911yescharacteristic, complemented
435#123—91no—
436#123—91no—
437#123—91no—
438#123—91no—
439C22⋊Q8—91no—
440C22⋊Q8—91no—
441C22⋊Q8—91no—
442#121—91no—
443C4×D4—91no—
444C4×D4—91no—
445C2×C4⋊C4—91no—
446C3×C9#53911yescharacteristic, complemented, Sylow
447C23×C3—91no—
448C23×C3—91no—
449C23×C3—91no—
450C22×D3—31no—
451C22×D3—31no—
452C22×D3—31no—
453C3×Q8—361no—
454C3×D4—182no—
455C3×D4—182no—
456C3×D4—361no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—91no—
465C2×C3×C4—91no—
466C2×C3×C4—91no—
467C2×C3×C4—91no—
468C2×C3×C4—91no—
469C2×C3×C4—182no—
470C2×C3×C4—361no—
471C2×C3×C4—361no—
472C2×C3×C4—361no—
473C2×C3×C4—361no—
474C2×C3×C4C22×D911yescharacteristic
475C2×C3×C4C22×D911yescharacteristic
476C2×C3×C4C22×D911yescharacteristic
477C2×C3×C4C22×D911yescharacteristic
478C2×C3×C4C22×D911yescharacteristic
479C2×C3×C4C22×D911yescharacteristic
480C2×C3×C4C22×D911yescharacteristic
481C2×C3×C4C22×C3×D311yescharacteristic
482C2×C3×C4C22×C3×D311yescharacteristic
483C2×C3×C4C22×C3×D311yescharacteristic
484C2×C3×C4C22×C3×D311yescharacteristic
485C2×C3×C4C22×C3×D311yescharacteristic
486C2×C3×C4C22×C3×D311yescharacteristic
487C2×C3×C4C22×C3×D311yescharacteristic
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493D12—62no—
494D12—62no—
495D12—121no—
496C4×D3—62no—
497C4×D3—121no—
498C4×D3—121no—
499C4×D3—121no—
500C4×D3—121no—
501Dic6—121no—
502C2×C32#100711yescharacteristic
503C2×C32D3×#4111yescharacteristic
504C2×C32#100911yescharacteristic
505C3×D3—62no—
506C3×D3—121no—
507C3×D3—121no—
508C2×C9—21no—
509C2×C9—21no—
510C2×C9—21no—
511C2×C9C2×C3×#4111yescharacteristic
512C2×C9C3×H(5,𝔽2)11yescharacteristic
513C2×C9C3×2−1+411yescharacteristic
514D9—22no—
515D9—41no—
516D9—41no—
517C2×Q8—91no—
518C2×D4—91no—
519C2×D4—91no—
520C2×D4—91no—
521C22×C4—91no—
522C22×C4—91no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—91no—
526C4⋊C4—91no—
527C4⋊C4—91no—
528C4⋊C4—91no—
529C4⋊C4—91no—
530C4⋊C4—91no—
531C4⋊C4—91no—
532C4⋊C4—91no—
533C4⋊C4—91no—
534C4⋊C4C2×C3×D911yescharacteristic
535C4⋊C4C2×C3×D911yescharacteristic
536C4⋊C4C2×C3×D911yescharacteristic
537C4⋊C4C2×C3×D911yescharacteristic
538C4⋊C4C2×C3×D911yescharacteristic
539C4⋊C4C2×C3×D911yescharacteristic
540C22⋊C4—91no—
541C22⋊C4—91no—
542C22⋊C4—91no—
543C22⋊C4—91no—
544C22⋊C4—91no—
545C22⋊C4—91no—
546C22⋊C4—91no—
547C22⋊C4—91no—
548C22⋊C4—91no—
549C22⋊C4—91no—
550C42—91no—
551C42C2×C3×D911yescharacteristic
552C22×C3—21no—
553C22×C3—92no—
554C22×C3—181no—
555C22×C3—181no—
556C22×C3—181no—
557C22×C3—181no—
558C22×C3—181no—
559C22×C3—181no—
560C22×C3—181no—
561C22×C3—181no—
562C22×C3C23×D911yescharacteristic
563C22×C3C23×C3×D311yescharacteristic
564C2×D3—32no—
565C2×D3—61no—
566C2×D3—61no—
567C2×D3—61no—
568C2×D3—61no—
569C2×D3—61no—
570C2×D3—61no—
571C2×D3—61no—
572C2×D3—61no—
573C3×C4—22no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—41no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—181no—
595C3×C4—181no—
596C3×C4—181no—
597C3×C4—181no—
598C3×C4—181no—
599Dic3—61no—
600Dic3—61no—
601Dic3—61no—
602Dic3—61no—
603Dic3—61no—
604C32#569211yescharacteristic
605C9—21no—
606C9C3×#53911yescharacteristic, complemented
607C23—91no—
608C23—91no—
609C23—91no—
610Q8—361no—
611D4—182no—
612D4—182no—
613D4—361no—
614C2×C4—91no—
615C2×C4—91no—
616C2×C4—91no—
617C2×C4—91no—
618C2×C4—91no—
619C2×C4—182no—
620C2×C4—361no—
621C2×C4—361no—
622C2×C4—361no—
623C2×C4—361no—
624C2×C4C22×C3×D911yescharacteristic
625C2×C4C22×C3×D911yescharacteristic
626C2×C4C22×C3×D911yescharacteristic
627C2×C4C22×C3×D911yescharacteristic
628C2×C4C22×C3×D911yescharacteristic
629C2×C4C22×C3×D911yescharacteristic
630C2×C4C22×C3×D911yescharacteristic
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—21no—
634C2×C3—182no—
635C2×C3—361no—
636C2×C3—361no—
637C2×C3#6371311yescharacteristic
638C2×C3#41×D911yescharacteristic
639C2×C3#6371511yescharacteristic
640C2×C3C3×#100711yescharacteristic
641C2×C3C3×D3×#4111yescharacteristic
642C2×C3C3×#100911yescharacteristic
643D3—62no—
644D3—121no—
645D3—121no—
646C22—92no—
647C22—181no—
648C22—181no—
649C22—181no—
650C22—181no—
651C22—181no—
652C22—181no—
653C22—181no—
654C22—181no—
655C22C23×C3×D911yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—21no—
661C4—21no—
662C4—21no—
663C4—181no—
664C4—181no—
665C4—181no—
666C4—181no—
667C4—181no—
668C3—21no—
669C3#1058979411yescharacteristic, direct product factor
670C3C3×#569211yescharacteristic
671C2—182no—
672C2—361no—
673C2—361no—
674C2C3×#6371311yescharacteristic
675C2C3×#41×D911yescharacteristic
676C2C3×#6371511yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#125C2
socleC22×C32C23×D3
prime radicalC3×#63457C2
hypercenterC3×#125D9
hypocenterC9C3×#539
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C9×#125C2semidirect
2. C3×#63460C2semidirect
3. C3×#63459C2semidirect
4. C3×#63458C2semidirect
5. C3×#63458C2semidirect
7. C3×#63456C2semidirect
8. C3×#63456C2semidirect
9. C3×#63456C2semidirect
10. C3×#63456C2semidirect
11. C3×#63455C2semidirect
12. C3×C4⋊C4×D9C2semidirect
13. C3×#63451C2semidirect
14. C3×#63438C2semidirect
15. C3×C4×D36C2semidirect
17. #10589794C3direct (N × H)
69. C9×#125C2×C3semidirect
70. #63460C2×C3semidirect
71. #63459C2×C3semidirect
72. #63458C2×C3semidirect
73. #63458C2×C3semidirect
75. #63456C2×C3semidirect
76. #63456C2×C3semidirect
77. #63456C2×C3semidirect
78. #63456C2×C3semidirect
79. #63455C2×C3semidirect
80. C4⋊C4×D9C2×C3semidirect
81. #63451C2×C3semidirect
82. #63438C2×C3semidirect
83. C4×D36C2×C3semidirect
213. C3×#125D9semidirect
434. #125C3×D9semidirect
446. C3×C9#539semidirect
606. C9C3×#539semidirect
669. C3#10589794direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C9×#1252
C3×#634602
C3×#634592
C3×#634582
C3×#634572
C3×#634562
C3×#634552
C3×C4⋊C4×D92
C3×#634512
C3×#634382
C3×C4×D362
C3×#56923
#105897943